Highest Common Factor of 784, 1536, 6874 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 784, 1536, 6874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 1536, 6874 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 784, 1536, 6874 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 784, 1536, 6874 is 2.
HCF(784, 1536, 6874) = 2
HCF of 784, 1536, 6874 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 784, 1536, 6874 is 2.
Highest Common Factor of 784,1536,6874 is 2
Step 1: Since 1536 > 784, we apply the division lemma to 1536 and 784, to get
1536 = 784 x 1 + 752
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 752 and 784, to get
784 = 752 x 1 + 32
Step 3: We consider the new divisor 752 and the new remainder 32, and apply the division lemma to get
752 = 32 x 23 + 16
We consider the new divisor 32 and the new remainder 16, and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 784 and 1536 is 16
Notice that 16 = HCF(32,16) = HCF(752,32) = HCF(784,752) = HCF(1536,784) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6874 > 16, we apply the division lemma to 6874 and 16, to get
6874 = 16 x 429 + 10
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 10 and 16, to get
16 = 10 x 1 + 6
Step 3: We consider the new divisor 10 and the new remainder 6, and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 6874 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(6874,16) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 784, 1536, 6874 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 784, 1536, 6874?
Answer: HCF of 784, 1536, 6874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 1536, 6874 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 1536, 6874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.